Answer to Question #46738 in Linear Algebra for ANURAG

Question

1. Show that: [ x l m 1]
[ a x n 1] = (x-a)(x-b)(x-c)
[ a b x 1]
[ a b c 1]

2. Show that: [ 1+ (a)^2 - (b)^2 2b -2b ]
[ 2ab 1 - (a)^2 + (b)^2 2a ]
[ 2b -2(a)^2 1 - (a)^2 - (b)^2 ]
is a perfect cube.

{please note that these are determinants, the first one is a 4X4 determinant and the second one is a 3X3 determinant}